Time-Splitting Chebyshev-Spectral Method for the Schrödinger Equation in the Semiclassical Regime with Zero Far-Field Boundary Conditions
Bibliographic record
Abstract
Abstract: Semiclassical limit of SchrA¶dinger equation with zero far-field boundary conditions is investigated by the time-splitting Chebyshev-spectral method. The numerical results of the position density and current density are presented. The time-splitting Chebyshev-spectral method is based on Strang splitting method in time coupled with Chebyshev-spectral approximation in space. Compared with the time-splitting Fourier-spectral method, the time-splitting Chebyshev-spectral method is unnecessary to treat the wave function as periodic and holds the smoothness of the wave function. For different initial conditions and potential (e.g. constant potential and harmonic potential), extensive numerical test examples in one-dimension are studied. The numerical results are in good agreement with the weak limit solutions. It shows that the time-splitting Chebyshev-spectral method is effective in capturing Iµ -oscillatory solutions of the SchrA¶dinger equation with zero far-field boundary conditions. In addition, the time-splitting Chebyshev-spectral method surpasses the traditional finite difference method in the meshing strategy due to the exponentially high-order accuracy of Chebyshev-spectral method.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".